Notes to Prolegomena to an Apology for Pragmaticism

531 * In his Logische Studien (1877)
  n1 In the original publication of this division, in 1867 [1.558] the term A "representamen" was employed in the sense of a sign in general, while A "sign" was taken as a synonym of Index, and an Icon was termed a A "likeness."
534 n1 You apprehend in what way the system of Existential Graphs is to furnish a test of the truth or falsity of Pragmaticism. Namely, sufficient study of the Graphs should show what nature is truly common_ to all significations of concepts; whereupon a comparison will show whether that nature be or be not the very ilk that Pragmaticism (by the definition of it) avers that it is. It is true that the two terms of this comparison, while in substance identical, yet might make their appearance under such different garbs that the student might fail to recognize their identity. At any rate, the possibility of such a result has to be taken into account; and therewith it must be acknowledged that, on its negative side, the argument may not turn out to be sufficient. For example, qua Graph, a concept might be regarded as the passive object of a geometrical intuitus, although Pragmaticism certainly makes the essence of every concept to be exhibited in an influence on possible conduct; and a student might fail to perceive that these two aspects of the concept are quite compatible.
But, on the other hand, should the theory of Pragmaticism be erroneous, the student would only have to compare concept after concept, each one, first, in the light of Existential Graphs, and then as Pragmaticism would interpret it, and it could not but be that before long he would come upon a concept whose analyses from these two widely separated points of view unmistakably conflicted. . . . - from "Phaneroscopy phav "; one of a number of fragmentary manuscripts designed to follow the present article. See 540n; 553n and 1. 306n.

535 * "Remarks on the Chemico-Algebraic Theory," Mathematical Papers, No. 28.
  ** (t) "Chemistry and Algebra," Mathematical Papers, vol. III, no. 14.
536 *  Signs can be classified on the basis of the characters which (l) they, (2) their immediate and (3) their dynamical objects, and their (4) immediate, (5) dynamical and (G) final interpretants possess, as well as on the basis of the nature of relations which (7) the dynamical objects and the (8) dynamical and (9) final interpret. ants have to the sign and which the (10) final interpretant has to the object. These ten divisions provide thirty designations for signs (each division being trichotomized by the categories, First, Second and Third). When properly arranged, they are easily shown to yield but sixty-six classes of possible signs. The principle determining that conclusion is stated in the introduction to vol. 2 and in 2. 235n. See also the letters to Lady Welby, vol. 9
  ** (7) of the previous footnote. Cf. 2. 243; 2. 247.
537 n1 Dr. Edward Eggleston originated the method.
  ** The type, token and tone are the legisigns, sinsigns and qualisigns discussed in 2. 243f and form division (l) in the note to 536.
538 * * These are defined in terms of the relation of the final interpretant to the sign. sign. They constitute division (9) in the note to 536 Cf 2.250f.
  ** Or rheme. But cf. 560
  *** Or dicisign.
539 * I.e., The perceptual judgment is a proposition of existence determined by the Percept, which it interprets. See 541, 5.115ff and 5.151ff.
  ** I.e., A complex of percepts yields a picture of a perceptual universe. With out refection, that universe is taken to be the cause of such objects as are represented in a percept. Though each percept is vague, as it is recognized that its object is the result of the action of the universe on the perceiver, it is so far clear.
540 * This is the last published article of the present series. A number of incompleted papers, intended as the next article, have been found and published in Part. See e.g., 1.305n, 1.306n, 534n, 553n, 5G1n, 564n, 5.549f.
541 n1 Abduction, in the sense I give the word, is any reasoning of a large class of which the provisional adoption of an explanatory hypothesis is the type. But it includes processes of thought which lead only to the suggestion of questions to be considered, and includes much besides.
543 * Cf. 2.407 ff.
  ** Cf. vol 2, bk II, ch.4.
544 n1 Strictly pure Symbols can signify only things familiar, and those only in so far as they are familiar.
  n2 I use the term Universe in a sense which excludes many of the so-called " universes of discourse " of which Boole [An Investigation of the Laws of Thought etc. pp. 42, 167], DeMorgan [Cambridge Philosophical Transactions VIII 380 Formal Logic, pp. 37-8] and many subsequent logicians speak, but which, being perfectly definable, would in the present system be denoted by the aid of a graph.
546 * 2.536.
547 * * E.g., in 1.422. See also 580.
  n1 I take it that anything may fairly be said to be destined when is sure to come about although there is no necessitating reason for it. Thus, a pair of dice thrown often enough, will be sure to turn up sixes some time, although there is no necessity that they should. The probability that they will is 1: that is all. Fate is that special kind of destiny by which events are supposed to be brought about under definite circumstances which involve no necessitating cause for those occurrences.
548 * The numeration has been changed to avoid ambiguity. Originally A, A', and I were all numbered 1; B, B', and 2 were all numbered 2, and not differentiated in the text.
  ** 3, 6, and 7 were all numbered 3; and 4, 6, and 8 were all numbered 4 in the original and not distinguished in the text.
  *** * Originally ". . . forms of statement of 3 and 4 on the other theory of the universes . . ."; a locution necessary so long as 3 and 5, and 4 and 6 were not distinguished.
  n1 In correcting the proofs, a good while after the above was written, I am obliged to confess that in some places the reasoning is erroneous; and a much simpler argument would nave supported the same conclusion more justly; though some weight ought to be accorded to my argument here, on the whole.
549 * Usually called categories by Peirce. See vol. 1, bk. III.
550 * I.e., Mind is a propositional function of the widest possible universe, such that its values are the meanings of all signs whose actual effects are in effective interconnection.
552 n1 They may be two bodies of persons, two persons, or two mental attitudes or states of one person.
  n2 A Graph has already been defined in 535 et seq.
  n3 The traditional and ancient use of the term Propositional Quality makes it an affair of the mode of expression solely. For "Socrates is mortal" and "Socrates is immortal" are equally Affirmative; "Socrates is not mortal" and "Socrates is not immortal" are equally Negative, provided "is not" translates non est. If, however, " is not" is in Latin est non, with no difference of meaning, the proposition is infinitated. Without anything but the merest verbiage to support the supposition that there is any corresponding distinction between different meanings of propositions, Kant insisted on raising the difference of expression to the dignity of a category. In [3.532; but cf. 5.450] I gave some reason for considering a relative proposition to be affirmative or negative according as it does or doe not unconditionally assert the existence of an indefinite subject. Although at the time of writing that, nine and a half years ago, I was constrained against my inclinations, to make that statement, yet I never heartily embraced that view and dismissed it from my mind, until after I had drawn up the present statement of the Conventions of Existential Graphs, I found quite to my surprise that I had herein taken substantially the same view. That is to say, although I herein speak only of "relative" quality, calling the assertion of any proposition the Affirmation of it, and regarding the denial of it as an assertion concerning that proposition as subject, namely, that it is false; which is my distinction of Quality Relative to the proposition either itself Affirmed, or of which the falsity is affirmed, if the Relative Quality of it is Negative, yet since every Graph in itself either recognizes the existence of a familiar Singular subject or asserts something of an indefinite subject asserted to exist in some Universe, it follows that every relatively Affirmative Graph unconditionally asserts or recognizes the occurrence of some description of object in some Universe; while no relatively Negative Graph does this. The logic of a Limited Universe of Marks [2.519ff.] suggests a different view of Quality, but careful analysis shows that it is in no fundamental conflict with the above.

A question not altogether foreign to the subject of Quality is whether Quality and Modality are of the same general nature. In selecting a mode of representing Modality, which I have not done without much experimentation I have finally resorted to one which commits itself as little as possible to any particular theory of the nature of Modality, although there are undeniable objections to such a course. If any particular analysis of Modality had appeared to me to be quite evident, I should have endeavored to exhibit it unequivocally. Meantime, my opinion is that the Universe is a Subject of every proposition and that any Modality shown by its indefiniteness to be Affirmative, such as Possibility and Intention, is a special determination of the Universe of The Truth. Something of this sort is seen in Negation. For if we say of a Man that he is not sinless, we represent the sinless as having a place only in an ideal universe which, or the part of which that contains the imagined sinless being, we then positively sever from the identity of the man in question.

553 n1 I may as well, at once, acknowledge that, in Existential Graphs, the representation of Modality (possibility, necessity, etc.) lacks almost entirely that pictorial, or Iconic, character which is so striking in the representation in the same system of every feature of propositions de inesse. Perhaps it is in the nature of things that it should be so in such wise that for Modality to be iconically represented in that same "pictorial" way in which the other features are represented would constitute a falsity in the representation. If so, it is a perfect vindication of the system, upon whose accusers, I suppose, the burden of proof lies. Still, I confess I suspect there is in the heraldic representation of modality as set forth [below] a defect capable of being remedied. rn it be not so, if the lack of "pictorialness" in the representation of modality cannot be remedied, it is because modality has, in truth, the nature which I opined it has (which opinion I expressed toward the end of the footnote [to 552]), and if that be the case, Modality is not, properly speaking, conceivable at all, but the difference, for example, between possibility and actuality is only recognizable much in the same way as we recognize the difference between a dream and waking experience, supposing the dream to be ever so detailed, reasonable, and thoroughly consistent with itself and with all the rest of the dreamer's experience. Namely, it still would not be so "vivid" as waking experience. . . - from "Phaneroscopy, phan," c. 1906; part of the manuscript used in 534n.
  n2 It was the genius of my gifted student, Dr. 0. H. Mitchell, in [Studies in Logic, ed. by C. S. Peirce, p. 73ff] that first opened our eyes to the identity of the subject of all assertions, although in another sense one assertion may have several individual subjects, which may even belong to what Mitchell called (quite justifiably, notwithstanding a certain condemnatory remark, as superficial as it was supercilious), different dimensions of the logical Universe. The entire Phemic Sheet and indeed the whole Leaf [see 555] is an image of the universal field of interconnected Thought (for, of course, all thoughts are interconnected). The field of Thought, in its turn, is in every thought, confessed to be a sign of that great external power, that Universe, the Truth. We all agree that we refer to the same real thing when we speak of the truth, whether we think aright of it, or not. But we have no cognition of its essence that can, in strictness, he called a concept of it: we only have a direct perception of having the matter of our Thought forced upon it from outside our own control. It is thus, neither by immediate feeling, as we gaze at a red color, that we mean what we mean by the Truth; for Feeling tells of nothing but itself. Nor is it by the persuasion of reason, since reason always refers to two other things than itself. But it is by what I call a dyadic consciousness.--from "The Bedrock beneath Pragmaticism," c. 1906, one of a number of fragmentary manuscripts designed to follow the present article.
  n3 It is chiefly for the sake of these convenient and familiar modes of representation of Petrosancta, that a modification of heraldic tinctures has been adopted. Vair and Potent here receive less decorative and pictorial Symbols. Fer and Plomb are selected to fill out the quaternion of metals on account of their monosyllabic names
556 n1 I am tempted to say that it is the reversal alone that effects the denial, the Cut merely cutting off the Graph within from assertion concerning the Universe to which the Phemic Sheet refers. But that is not the only possible view, and it would be rash to adopt it definitely, as yet.
558 n1 For, of course, the Graph-instance must be on one sheet; and if part were on the recto, and part on the verso, it would not be on one continuous sheet. On the other hand, a Graph-instance can perfectly well extend from one Province to another, and even from one Realm (or space having one Mode of Tincture) to another. Thus, the Spot, "-is in the relation-to-" may if the relation is that of an existent object to its purpose, have the first Peg on Metal the second on Color, and the third on Fur. Cf. 579.
561 n1 The essential error, to protov yeudos, of the Selectives, and their inevitable error, to prwtov yeudos, lies in their putting forth, in a system which aims at giving, in its visible forms, a diagram of the logical structure of assertions, as a representation, for example, of the assertion that Tully and Cicero are the same man, a type of image which does not differ in form from the assertion that Julius Caesar and Louis Seize were both men:

. . . The purpose of the System of Existential Graphs, as it is stated in the Prolegomena [533], [is] to afford a method (l) as simple as possible that is to say, with as small a number of arbitrary conventions as possible), for representing propositions (2) as iconicalLy, or diagrammatically and<x3) as analytically as possible. The reason for embracing this purpose was developed through the first dozen pages of this paper.) These three essential aims of the system are, every one of them, missed by Selectives. The first, that of the utmost attain- able simplicity, is so, since a selective cannot be used without being attached to a Ligature, and Ligatures without Selectives will express all that Selectives with Ligatures express. The second aim, to make the representations as iconical as possible is likewise missed; since Ligatures are far more iconic than Selectives. For the comparison of the above figures shows that a Selective can only serve its purpose through a special habit of interpretation that is otherwise needless in the system, and that makes the Selective a Symbol and not an Icon; while a Ligature expresses the same thing as a necessary consequence regarding each sizeable dot as an Icon of what we call an "individual object"; and it must be such an Icon if we are to regard an invisible mathematical point as an Icon of the strict individual, absolutely determinate in all respects, which imagination cannot realize. Meantime, the fact that a special convention (a clause of the fourth) is required to distinguish a Selective from an ordinary univalent Spot constitutes a second infraction of the purpose of simplicity. The third item of the idea of the System, that of being as analytical as possible, is in- fringed by Selectives in no less than three ways. This, at least, is the case if it be true as I shall endeavour further on to convince the reader that it is, that Concepts are capable of being compounded only in a way differing but in one doubtful particular from that in which the so-called "substances"--i.e., species--of Organic Chemistry are compounded, according to the established theory of that science. (That respect is that the different bonds and pegs of the Spots of Graphs are different, while those of chemical atoms are believed to be all alike. But on the one hand, it may possibly be that a more nearly ultimate analysis of Concepts would show, as Kempe's "A Memoir on the theory of Mathematical Form" [Philosophical Transactions of the Royal Society, v. 177, pp. 1-70, 1886] seems to think, that the pegs of simple concepts are all alike. On the other hand, the carbon-atom seems to be the only one for the entire similarity of whose bonds there is much positive evidence. In the case of nitrogen, for example two of the five valencies seem to be of such different quality from the others as to suggest that the individual bonds may likewise be different; and if there were such difference between different bonds of atoms generally obvious probable causes would prevent our discovering [them] in the present state of chemistry Looking at the question from the point of view of Thomson's corpuscles, it seems very unlikely that the looser electrons all fulfill precisely the same function in all cases.) For if this be true the fact that two or more given concepts <an be put together to produce one concept, without either of those that are so put together being separated into parts, is concLusive proof that the concept so produced is a compound of those that were put together. The principle, no doubt, requires to be proved. For it might easily be thought that the concept of a scalar as well as that of a vector (in quaternions) can equally result from putting together the concepts of a tensor and a versor in different ways, while at the same time the concept of a tensor and that of a versor can, in their turn, result from putting tog<xher those of a scalar and of a vector in different ways; so that no one of the four concepts is more or less composite than any of the others.

Were such a view borne out by exact analysis, as it certainly is not, a radical disparateness between the composition of concepts and that of chemical species would be revealed. But this could scarcely fail to entail such a serious revolution in accepted doctrines of logic as it would be unwarrantable gratuitously to suppose that further investigation will bring about. It will be found that the available evidence is decidedly that Concepts can only be combined through definite "pegs." The first respect in which Selectives are not as analytical as they might be, and therefore ought to be, is in representing identity. The identity of the two S's above is only symbolically expressed... Iconically, they appear to be merely coexistent; but by the special convention they are interpreted as identical, though identity is not a matter of interpretation--that is of logical depth--but is an assertion of unity of Object, that is, is an assertion regarding logical breadth. The two S's are instances of one symbol, and that of so peculiar a kind that they are interpreted as signifying, and not merely denoting, one individual. There is here no analysis of identity. The suggestion, at least, is, quite decidedly, that identity is a simple relation. The line of identity which may be substituted for the selectives very explicitly represents Identity to belong to the genus Continuity and to the species Linear Continuity. But of what variety of Linear Continuity is the heavy line more especially the Icon in the System of Existential Graphs? In order to ascertain this, let us contrast the Iconicity of the line with that of the surface of the Phemic Sheet. The continuity of this surface being two-dimensional, and so polyadic should represent an external continuity, and especially, a continuity of experiential appearance. Moreover, the Phemic Sheet iconizes the Universe of Discourse since it more immediately represents a field of Thought, or Mental Experience, which is itself directed to the Universe of Discourse, and considered as a sign, denotes that Universe. Moreover, it [is because it must be understood] as being directed to that Universe, that it is iconized by the Phemic Sheet. So, on the principle that logicians call "the Nota notae" that the sign of anything, X, is itself a sign of the very same X, the Phemic Sheet, in representing the field of attention represents the general object of that attention, the Universe of Discourse. This being the case, the continuity of the Phemic Sheet in those places, where, nothing being being scribed, no particular attention is paid, is the most appropriate Icon possible of the continuity of the Universe of Discourse where it only receives general attention as that Universe - that is to say of the continuity in experiential appearance of the Universe, relatively to any objects represented as belonging to it.--From "The Bedrock beneath Pragmaticism" (2) 1906; one of a number of fragmentary manuscripts designed to follow the present article.

563 n1 It is Permissible to have such spots as "possesses the character " "is in the real relation to," but it is not permissible to have such a spot as "can prevent the existence of."
564 * Vol. 3, No. XVI, 4.
  n1 I can make this blackened Inner Close as small as I please, at least, so long as I can still see it there, whether with my outer eye or in my mind's eye. Can I not make it quite invisibly small, even to my mind's eye? "No" you will say "for then it would not be scribed at all." You are right. Yet since confession will be good for my soul, and since it will be well for you to learn how like walking on smooth ice this business of reasoning about logic is--so much so that I have often remarked that nobody commits what is called a "logical fallacy" or hardly ever does so, except logicians; and they are slumping into such stuff continually--it is my duty to [point out) this error of assuming that, because the blackened Inner Close can be made indefinitely small, therefore it can be struck out entirely like an infinitesimal. That led me to say that a Cut around a Graph-instance has the effect of denying it. I retract: it only does so if the Cut enclosed also [has] a blot, however small, to represent iconically, the blackened Inner Close. I was partly misled by the fact that in the Conditional de inesse the Cut may be considered as denying the contents of its Area. That is true, so long as the entire Scroll is on the Place. But that does not prove that a single Cut without an Inner Close, has this effect. On the contrary, a single Cut, enclosing only A and a blank, merely says: "If A," or "If A, then" and there stops If what? you ask. It does not say. "Then something follows," perhaps; but there is no assertion at all. This can be proved, too. For if we scribe on the Phemic Sheet the Graph expressing "If A is true, Something is true," we shall have a Scroll with A alone in the Outer Close, and with nothing but a Blank in the Inner Close. Now this Blank is an Iterate of the Blank-instance that is always present on the Phemic Sheet; and this may, according to the rule, be deiterated by removing the Blank in the inner close. This will do, what the blot would not; namely, it will cause the collapse of the Inner Close, and thus leaves A in a single cut. We thus see that a Graph, A, enclosed in a single Cut that contains nothing else but a Blank has no signification that is not implied in the proposition "If A is true, Something is true." When I was in the twenties and had not yet come to the full consciousness of my own gigantic powers of logical blundering, with what scorn I used to think of Hegel's confusion of Being with Blank Nothing, simply because it had the form of a predicate without its matter! Yet here am I after devoting a greater number of years to the study of exact logic than the probable number of hours that Hegel ever gave to this subject, repeating that very identical fallacy! Be sure, Reader, that I would have concealed the mistake from you (for vanity's sake, if for no better reason), if it had not been "up to" me, in a way I could not evade, to expose it.--From "Copy T" c. 1906; one of a number of fragmentary manuscripts designed to follow the present article.
569 * Cf. 580.
  ** In a letter to F. A. Woods, in 1913, Peirce expressed scepticism as to the universal validity of this permission--see vol [8, p. 297-8]. See also 580.
572 * See 540n.